Sylow子-群的正规化子具有一定性质的有限群的结构

Structure of Some Finite Groups with Certain Normalizers of Sylow Subgroups

对子群的正规化子具有一定性质的有限可解群的结构进行了探讨,获得了2个主要结果:可解群G是幂零群当且仅当对p∈π(G),NG(Gp)为p-幂零群;给出了可解群G的部分给定指数的Sylow子-群的正规化子是幂零群的G结构.

The structure of finite groups with certain normalizers of sylow subgroups is characterized. Two main results are obtained ： （ 1 ） A soluble group G is nilpotent group if and only if A↓p∈π（G）, Nc （Gp） is a p-nilpotent group. （2）The structure of finite soluble groups with some nilpotent normalizers of Sylow subgroups is discussed.